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Question
Prove that:
\[\frac{7\pi}{12} + \cos\frac{\pi}{12} = \sin\frac{5\pi}{12} - \sin\frac{\pi}{12}\]
Solution
LHS = cos105o + cos15o
= cos(90o + 15o) + cos(90o - 75o)
= - sin 15o + sin 75o [As cos(90o+A) = - sin A and cos(90o- B) = sin B]
= sin 75o- sin 15o
= RHS
Hence proved.
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